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template<class Real> class sinh_sinh { public: sinh_sinh(size_t max_refinements = 9); template<class F> auto integrate(const F f, Real tol = sqrt(std::numeric_limits<Real>::epsilon()), Real* error = nullptr, Real* L1 = nullptr, size_t* levels = nullptr)->decltype(std::declval<F>()(std::declval<Real>())) const;; };
The sinh-sinh quadrature allows computation over the entire real line, and is called as follows:
sinh_sinh<double> integrator; auto f = [](double x) { return exp(-x*x); }; double error; double L1; double Q = integrator.integrate(f, &error, &L1);
Note that the limits of integration are understood to be (-∞, +∞).
Complex valued integrands are supported as well, for example the Dirichlet Eta function can be represented via:
which we can directly code up as:
template <class Complex> Complex eta(Complex s) { typedef typename Complex::value_type value_type; using std::pow; using std::exp; Complex i(0, 1); value_type pi = boost::math::constants::pi<value_type>(); auto f = [&, s, i](value_type t) { return pow(0.5 + i * t, -s) / (exp(pi * t) + exp(-pi * t)); }; boost::math::quadrature::sinh_sinh<value_type> integrator; return integrator.integrate(f); }